[ceph.git] / ceph / src / boost / libs / math / test / test_legendre.hpp

// Copyright John Maddock 2006.
// Copyright Paul A. Bristow 2007, 2009
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifdef _MSC_VER
#  pragma warning (disable : 4756) // overflow in constant arithmetic
#endif

#include <boost/math/concepts/real_concept.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/special_functions/math_fwd.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/array.hpp>
#include "functor.hpp"

#include "handle_test_result.hpp"
#include "table_type.hpp"

#ifndef SC_
#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
#endif

template <class Real, class T>
void do_test_legendre_p(const T& data, const char* type_name, const char* test_name)
{
   typedef Real                   value_type;

   typedef value_type (*pg)(int, value_type);
   pg funcp;

#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_P_FUNCTION_TO_TEST))
#ifdef LEGENDRE_P_FUNCTION_TO_TEST
   funcp = LEGENDRE_P_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   funcp = boost::math::legendre_p<value_type>;
#else
   funcp = boost::math::legendre_p;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test legendre_p against data:
   //
   result = boost::math::tools::test_hetero<Real>(
      data,
      bind_func_int1<Real>(funcp, 0, 1),
      extract_result<Real>(2));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p", test_name);
#endif

   typedef value_type (*pg2)(unsigned, value_type);
#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_Q_FUNCTION_TO_TEST))
#ifdef LEGENDRE_Q_FUNCTION_TO_TEST
   pg2 funcp2 = LEGENDRE_Q_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg2 funcp2 = boost::math::legendre_q<value_type>;
#else
   pg2 funcp2 = boost::math::legendre_q;
#endif

   //
   // test legendre_q against data:
   //
   result = boost::math::tools::test_hetero<Real>(
      data,
      bind_func_int1<Real>(funcp2, 0, 1),
      extract_result<Real>(3));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_q", test_name);

   std::cout << std::endl;
#endif
}

template <class Real, class T>
void do_test_assoc_legendre_p(const T& data, const char* type_name, const char* test_name)
{
#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_PA_FUNCTION_TO_TEST))
   typedef Real                   value_type;

   typedef value_type (*pg)(int, int, value_type);
#ifdef LEGENDRE_PA_FUNCTION_TO_TEST
   pg funcp = LEGENDRE_PA_FUNCTION_TO_TEST;
#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
   pg funcp = boost::math::legendre_p<value_type>;
#else
   pg funcp = boost::math::legendre_p;
#endif

   boost::math::tools::test_result<value_type> result;

   std::cout << "Testing " << test_name << " with type " << type_name
      << "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";

   //
   // test legendre_p against data:
   //
   result = boost::math::tools::test_hetero<Real>(
      data,
      bind_func_int2<Real>(funcp, 0, 1, 2),
      extract_result<Real>(3));
   handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p (associated)", test_name);
   std::cout << std::endl;
#endif
}

template <class T>
void test_legendre_p(T, const char* name)
{
   //
   // The actual test data is rather verbose, so it's in a separate file
   //
   // The contents are as follows, each row of data contains
   // three items, input value a, input value b and erf(a, b):
   //
#  include "legendre_p.ipp"

   do_test_legendre_p<T>(legendre_p, name, "Legendre Polynomials: Small Values");

#  include "legendre_p_large.ipp"

   do_test_legendre_p<T>(legendre_p_large, name, "Legendre Polynomials: Large Values");

#  include "assoc_legendre_p.ipp"

   do_test_assoc_legendre_p<T>(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values");

}

template <class T>
void test_spots(T, const char* t)
{
   std::cout << "Testing basic sanity checks for type " << t << std::endl;
   //
   // basic sanity checks, tolerance is 100 epsilon:
   //
   T tolerance = boost::math::tools::epsilon<T>() * 100;
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance);

   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
   if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
   {
      BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
   }
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
   if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
   {
      BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
   }
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance);

   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance);
   BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance);
}
Commit	Line	Data
7c673cae FG	1	// Copyright John Maddock 2006.
	2	// Copyright Paul A. Bristow 2007, 2009
	3	// Use, modification and distribution are subject to the
	4	// Boost Software License, Version 1.0. (See accompanying file
	5	// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
	6
	7	#ifdef _MSC_VER
	8	# pragma warning (disable : 4756) // overflow in constant arithmetic
	9	#endif
	10
	11	#include <boost/math/concepts/real_concept.hpp>
	12	#define BOOST_TEST_MAIN
	13	#include <boost/test/unit_test.hpp>
	14	#include <boost/test/floating_point_comparison.hpp>
	15	#include <boost/math/special_functions/math_fwd.hpp>
	16	#include <boost/math/constants/constants.hpp>
	17	#include <boost/array.hpp>
	18	#include "functor.hpp"
	19
	20	#include "handle_test_result.hpp"
	21	#include "table_type.hpp"
	22
	23	#ifndef SC_
	24	#define SC_(x) static_cast<typename table_type<T>::type>(BOOST_JOIN(x, L))
	25	#endif
	26
	27	template <class Real, class T>
	28	void do_test_legendre_p(const T& data, const char* type_name, const char* test_name)
	29	{
	30	typedef Real value_type;
	31
	32	typedef value_type (*pg)(int, value_type);
	33	pg funcp;
	34
	35	#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_P_FUNCTION_TO_TEST))
	36	#ifdef LEGENDRE_P_FUNCTION_TO_TEST
	37	funcp = LEGENDRE_P_FUNCTION_TO_TEST;
	38	#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
	39	funcp = boost::math::legendre_p<value_type>;
	40	#else
	41	funcp = boost::math::legendre_p;
	42	#endif
	43
	44	boost::math::tools::test_result<value_type> result;
	45
	46	std::cout << "Testing " << test_name << " with type " << type_name
	47	<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
	48
	49	//
	50	// test legendre_p against data:
	51	//
	52	result = boost::math::tools::test_hetero<Real>(
	53	data,
	54	bind_func_int1<Real>(funcp, 0, 1),
	55	extract_result<Real>(2));
	56	handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p", test_name);
	57	#endif
	58
	59	typedef value_type (*pg2)(unsigned, value_type);
	60	#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_Q_FUNCTION_TO_TEST))
	61	#ifdef LEGENDRE_Q_FUNCTION_TO_TEST
	62	pg2 funcp2 = LEGENDRE_Q_FUNCTION_TO_TEST;
	63	#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
	64	pg2 funcp2 = boost::math::legendre_q<value_type>;
65	#else
66	pg2 funcp2 = boost::math::legendre_q;
67	#endif
68
69	//
70	// test legendre_q against data:
71	//
72	result = boost::math::tools::test_hetero<Real>(
73	data,
74	bind_func_int1<Real>(funcp2, 0, 1),
75	extract_result<Real>(3));
76	handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_q", test_name);
77
78	std::cout << std::endl;
79	#endif
80	}
81
82	template <class Real, class T>
83	void do_test_assoc_legendre_p(const T& data, const char* type_name, const char* test_name)
84	{
85	#if !(defined(ERROR_REPORTING_MODE) && !defined(LEGENDRE_PA_FUNCTION_TO_TEST))
86	typedef Real value_type;
87
88	typedef value_type (*pg)(int, int, value_type);
89	#ifdef LEGENDRE_PA_FUNCTION_TO_TEST
90	pg funcp = LEGENDRE_PA_FUNCTION_TO_TEST;
91	#elif defined(BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS)
92	pg funcp = boost::math::legendre_p<value_type>;
93	#else
94	pg funcp = boost::math::legendre_p;
95	#endif
96
97	boost::math::tools::test_result<value_type> result;
98
99	std::cout << "Testing " << test_name << " with type " << type_name
100	<< "\n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\n";
101
102	//
103	// test legendre_p against data:
104	//
105	result = boost::math::tools::test_hetero<Real>(
106	data,
107	bind_func_int2<Real>(funcp, 0, 1, 2),
108	extract_result<Real>(3));
109	handle_test_result(result, data[result.worst()], result.worst(), type_name, "legendre_p (associated)", test_name);
110	std::cout << std::endl;
111	#endif
112	}
113
114	template <class T>
115	void test_legendre_p(T, const char* name)
116	{
117	//
118	// The actual test data is rather verbose, so it's in a separate file
119	//
120	// The contents are as follows, each row of data contains
121	// three items, input value a, input value b and erf(a, b):
122	//
123	# include "legendre_p.ipp"
124
125	do_test_legendre_p<T>(legendre_p, name, "Legendre Polynomials: Small Values");
126
127	# include "legendre_p_large.ipp"
128
129	do_test_legendre_p<T>(legendre_p_large, name, "Legendre Polynomials: Large Values");
130
131	# include "assoc_legendre_p.ipp"
132
133	do_test_assoc_legendre_p<T>(assoc_legendre_p, name, "Associated Legendre Polynomials: Small Values");
134
135	}
136
137	template <class T>
138	void test_spots(T, const char* t)
139	{
140	std::cout << "Testing basic sanity checks for type " << t << std::endl;
141	//
142	// basic sanity checks, tolerance is 100 epsilon:
143	//
144	T tolerance = boost::math::tools::epsilon<T>() * 100;
145	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(1, static_cast<T>(0.5L)), static_cast<T>(0.5L), tolerance);
146	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-1, static_cast<T>(0.5L)), static_cast<T>(1L), tolerance);
147	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, static_cast<T>(0.5L)), static_cast<T>(-0.2890625000000000000000000000000000000000L), tolerance);
148	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, static_cast<T>(0.5L)), static_cast<T>(-0.4375000000000000000000000000000000000000L), tolerance);
149	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, static_cast<T>(0.5L)), static_cast<T>(0.2231445312500000000000000000000000000000L), tolerance);
150	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, static_cast<T>(0.5L)), static_cast<T>(0.3232421875000000000000000000000000000000L), tolerance);
151	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, static_cast<T>(0.5L)), static_cast<T>(-0.09542943523261546936538467572384923220258L), tolerance);
152	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, static_cast<T>(0.5L)), static_cast<T>(-0.1316993126940266257030910566308990611306L), tolerance);
153
154	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
155	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(0.5L)), static_cast<T>(5.625000000000000000000000000000000000000L), tolerance);
156	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
157	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
158	if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
159	{
160	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
161	}
162	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(0.5L)), static_cast<T>(4.966634149702370788037088925152355134665e30L), tolerance);
163	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, 2, static_cast<T>(-0.5L)), static_cast<T>(4.218750000000000000000000000000000000000L), tolerance);
164	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, 2, static_cast<T>(-0.5L)), static_cast<T>(-5.625000000000000000000000000000000000000L), tolerance);
165	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, 5, static_cast<T>(-0.5L)), static_cast<T>(-5696.789530152175143607977274672800795328L), tolerance);
166	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, 4, static_cast<T>(-0.5L)), static_cast<T>(465.1171875000000000000000000000000000000L), tolerance);
167	if(std::numeric_limits<T>::max_exponent > std::numeric_limits<float>::max_exponent)
168	{
169	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, 30, static_cast<T>(-0.5L)), static_cast<T>(-7.855722083232252643913331343916012143461e45L), tolerance);
170	}
171	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, 20, static_cast<T>(-0.5L)), static_cast<T>(-4.966634149702370788037088925152355134665e30L), tolerance);
172	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(4, -2, static_cast<T>(0.5L)), static_cast<T>(0.01171875000000000000000000000000000000000L), tolerance);
173	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-4, -2, static_cast<T>(0.5L)), static_cast<T>(0.04687500000000000000000000000000000000000L), tolerance);
174	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(7, -5, static_cast<T>(0.5L)), static_cast<T>(0.00002378609812640364935569308025139290054701L), tolerance);
175	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-7, -4, static_cast<T>(0.5L)), static_cast<T>(0.0002563476562500000000000000000000000000000L), tolerance);
176	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(40, -30, static_cast<T>(0.5L)), static_cast<T>(-2.379819988646847616996471299410611801239e-48L), tolerance);
177	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_p(-40, -20, static_cast<T>(0.5L)), static_cast<T>(4.356454600748202401657099008867502679122e-33L), tolerance);
178
179	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(1, static_cast<T>(0.5L)), static_cast<T>(-0.7253469278329725771511886907693685738381L), tolerance);
180	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(4, static_cast<T>(0.5L)), static_cast<T>(0.4401745259867706044988642951843745400835L), tolerance);
181	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(7, static_cast<T>(0.5L)), static_cast<T>(-0.3439152932669753451878700644212067616780L), tolerance);
182	BOOST_CHECK_CLOSE_FRACTION(::boost::math::legendre_q(40, static_cast<T>(0.5L)), static_cast<T>(0.1493671665503550095010454949479907886011L), tolerance);
183	}
184